I agree that many pages do not work properly with one or other browser. often I have problems myself for personal use, usually with chrome ( after they have done an update) Before using add ons, be very sure you know what you are doing and using them for. As long as you understand that pages might stuff up with add ons installed then great.
I am a amateur web manager for a veteran society, I know nothing (much) of html and use a wysiwyg developer tool for design and editing of web pages and site structure. I do this for two sites. As I am fully aware of how badly some browsers stuff up or fail to render web pages correctly I have installed on both my computers IE, Chrome, Firefox, Safari, the 4 'main' browsers that people mainly use and I check each page before it goes live through each to make sure they work.
Because these days some web developers allow you to use any font, or utility you like to make your page. If I used say a font that was not web safe for a browser my page would look dreadful on a visitors page if they did not have the same font installed. The same with flash or shockwave, silverlight etc, if they aren't installed or updated on the viewers browser(s) then they wont work and will make the webpage behave incorrectly.
All in all the only way around webpages not working is to keep everything updated and use at least 2 that you are comfortable and familiar with, that way if something does go wrong you will be able to see if its the website the internet connection or your browser and its add ons/extensions. Dont always blame web page designers for flaws, most of us check and double check our work before releasing it to make sure it works.

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